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On Banach spaces of the form \(C_0(\alpha \times L)\) with few operators

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Abstract

For an exotic locally compact Hausdorff space L, constructed under the assumption of Ostaszewski’s \(\clubsuit \)-principle, and a countable ordinal space \(\alpha \), we prove that all operators defined on \(C_0(\alpha \times L)\) have the simplest possible form. We also investigate the geometry of such space \(C_0(\alpha \times L)\) and we classify up to isomorphisms all its complemented subspaces.

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Acknowledgements

The author is greatly indebted with Prof. Piotr Koszmider from Institute of Mathematics of the Polish Academy of Sciences for suggestions and help. The author also thanks the referee for his careful reading and suggestions that greatly improved the original manuscript. The author was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP No. 2016/25574-8.

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  1. Departamento de Matemática, Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo-UNIFESP, São José dos Campos, SP, Brazil

    Leandro Candido

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  1. Leandro Candido
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Correspondence to Leandro Candido.

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Communicated by Krzysztof Jarosz.

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Candido, L. On Banach spaces of the form \(C_0(\alpha \times L)\) with few operators. Banach J. Math. Anal. 15, 41 (2021). https://doi.org/10.1007/s43037-021-00126-w

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  • DOI: https://doi.org/10.1007/s43037-021-00126-w

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